Decompositions and models for Hilbert-space operators have been active research topics in recent years, and this book is intended as an introduction to this area of operator theory, working from an abstract point of view. The approach is elementary in that all the proofs only use standard results of single operator thoery, although many of the questions posed in the text lead on to open problems.
An Introduction to Models and Decompositions in Operator...
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5 of 5 people found the following review helpful:
5.0 out of 5 stars
Nice and well organized introduction to a difficult subject,
This review is from: An Introduction to Models and Decompositions in Operator Theory (Hardcover)
The book is a very nice introduction to the subject of Models and Decompositions of operators. In reality, it is a post-introductory book. Anyone that has already studied operator Theory in Hilbert spaces and wants a deeper understanding of this subject, should have a look here, mainly because the book coherently organizes this subject that would otherwise require a large bibliographical research. Models and Decompositons are looked as a sub-product of the search for the "Holy Graal" of operator theory: The Invariant Subspace Problem. Although it is not a book about that subject, it is certainly a relevant book to anyone entering that field, because it mentions relatively recent results that were previously conjectures in that area. Particularly interesting, in my opinion, are chapters 7 and 8. Chapter 7, called "Applications", in which the theory developed in the previous chapters is applied and many interesting related problems, some of them still open, relative to strong and weak stability of operators are mentioned. Chapter 8 discusses the problem of similarity to contractions, and leaves the reader with two related open questions.
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Inside This Book
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First Sentence:
Throughout these notes all Hilbert spaces are nonzero, complex and separable. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
completely nonunitary isometry, strongly stable contraction, backward unilateral shift, canonical unilateral shift, contractions quasisimilar, nontrivial hyperinvariant subspace, cohyponormal contraction, unilateral shift acting, quasiaffine transform, unitary direct summand, nontrivial invariant subspace, completely nonunitary contraction, power bounded operator, power boundedness, nonnegative contraction, bilateral shift, nonunitary contractions, reducing subspace, hyponormal operators, polynomial boundedness, invariant subspace problem, subnormal operators, strict contraction, unilateral shifts, surjective isometry Key Phrases - Capitalized Phrases (CAPs): (learn more)
Banach-Steinhaus Theorem, Proof Let New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Throughout these notes all Hilbert spaces are nonzero, complex and separable. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
completely nonunitary isometry, strongly stable contraction, backward unilateral shift, canonical unilateral shift, contractions quasisimilar, nontrivial hyperinvariant subspace, cohyponormal contraction, unilateral shift acting, quasiaffine transform, unitary direct summand, nontrivial invariant subspace, completely nonunitary contraction, power bounded operator, power boundedness, nonnegative contraction, bilateral shift, nonunitary contractions, reducing subspace, hyponormal operators, polynomial boundedness, invariant subspace problem, subnormal operators, strict contraction, unilateral shifts, surjective isometry Key Phrases - Capitalized Phrases (CAPs): (learn more)
Banach-Steinhaus Theorem, Proof Let New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 21
books:
See all 21 books this book cites
2
books
cite this book:
- Lectures on Hyponormal Operators (Operator Theory Advances and Applications) by Mircea Martin in Back Matter (1), and Back Matter (2)
- The Theory of Subnormal Operators (Mathematical Surveys and Monographs) by John B. Conway in Back Matter
- Linear Operator Theory in Engineering and Science (Applied Mathematical Sciences) by Arch W. Naylor in Back Matter
- Functional Analysis (Dover Books on Mathematics) by George Bachman in Back Matter
- Introduction to Hilbert Space by P. R. Halmos in Back Matter
See all 21 books this book cites
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